Solvable-extensible automorphism

This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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This is a variation of extensible automorphism|Find other variations of extensible automorphism |

This term is related to: Extensible automorphisms problem
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Definition

Symbol-free definition

An automorphism of a solvable group is said to be solvable-extensible if it can be extended to an automorphism for any embedding of the given solvable group in a solvable group.

Definition with symbols

Let $G$ be a solvable group and $\sigma$ an automorphism of $G$. Then $\sigma$ is said to be solvable-extensible if for any embedding of $G</ma/th>inasolvablegroup<math>H$, there exists an automorphism $\phi$ of $H$ whose restriction to $G$ is $\sigma$.

Relation with other properties=

Stronger properties

• Extensible automorphism when the underlying group is solvable

Weaker properties

• Nilpotent-extensible automorphism when the underlying group is nilpotent